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Using tropical geometry, Block-Göttsche defined polynomials with the remarkable property to interpolate between Gromov-Witten counts of complex curves and Welschinger counts of real curves in toric del Pezzo surfaces. I will describe a generalization of Block-Göttsche polynomials to arbitrary, not-necessarily toric, rational surfaces and propose a conjectural relation with refined Donaldson-Thomas invariants. This is joint work with Hulya Arguz.
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